(Corrects fourth paragraph to show Musk was agreeing with a comment from another person on Twitter, not making the comment himself)

Aug 7 (Reuters) - Chief Executive Elon Musk said on Twitter he is considering taking Tesla Inc private at $420 per share as the electric car maker faces the challenges of fast growth and financial constraints, sending its shares up more than 6 percent.

At $420 per share, a deal would represent a 22.8 percent premium to Tesla’s closing price on Monday, making it one of the biggest go-private deals with a price tag of about $72 billion.

When another person tweeted that going private “saves a lot of headaches,” Musk replied, “Yes”.

Tesla did not immediately respond to a request for clarification.

Tesla’s shares jumped to $362.74 in afternoon trading. The company had a market value of $58 billion as of Monday’s close. Musk owns nearly 20 percent of the company.

Earlier in the day, the Financial Times reported that Saudi Arabia’s sovereign wealth fund, overseen by Crown Prince Mohammed bin Salman, has built an undisclosed stake of between 3 and 5 percent stake in Tesla.

Musk has been under intense pressure this year to prove he can deliver on his promise to turn his money-losing company into a profitable higher-volume manufacturer, a goal that has propped up Tesla shares and resulted in a market value higher than that of General Motors Co.

“I believe Tesla considers Tweets as public disclosure. I think he’s serious. Plus this is short squeeze rocket fuel after a nice quarter,” said analyst Chaim Siegel from Elazar Advisors.

A short squeeze is a trading scenario that occurs from time to time in heavily shorted stocks, when bearish traders are forced to buy shares to avoid big losses - something that ends up pushing the stock only higher.

Short interest in Tesla on Monday stood at nearly $12 billion, equivalent to 28 percent of its float, according to S3 Partners, a financial analytics firm.

The U.S. Securities and Exchange Commission allows companies to use social media outlets like Facebook and Twitter to announce key information in compliance with its fair disclosure rules so long as investors have been alerted about which social media outlets will be used to disseminate such information.

The SEC did not immediately respond to a request for comment on Musk’s tweet.

George Galliers of Evercore ISI said he believed the tweet was serious.

“I can’t believe this is something to bluff or make fun of. Given his historic frustration with short sellers, analysts and certain parts of the press, it is perhaps also not surprising that he has given consideration to taking the company private,” Galliers said.

“Details, structure, participants and how the valuation has been determined remain to be seen.” (Reporting by Sonam Rai in Bengaluru, Alexandria Sage in San Francisco and Pete Schroeder in Washington; editing by Saumyadeb Chakrabarty)